The boards of Deutsche Telekom AG and MetroPCS Communications Inc. have approved a deal to merge MetroPCS with the German operator’s U.S. subsidiary, T-Mobile USA, people familiar with the matter said Wednesday, a deal that would give the fourth-largest U.S. wireless carrier more scale as it tries to compete with the industry’s leaders.

The move further consolidates the U.S. wireless industry, but in a way that is likely to be well received by regulators, who last year shot down T-Mobile’s $39 billion deal to be acquired by AT&T Inc. to avoid reducing the ranks of national carriers from four to three.

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